When asking her about the Sarano Tomb she will trigger the quest and say:

A hunger has violated the Sarano Tomb. Go to this tomb which is over the hills southeast of Fort Moonmoth between the Ashlands and Lake Amaya, and kill the hunger.

Travel to Fort Moonmoth and then head on the path that cuts through the mountains to the south-east. Follow this and the turn left where the path splits at the lake. Follow this for a short distance looking for the Sarano Tomb entrance built into the mountain (this location can be difficult to spot, it is south east of Fort Moonmoth and close to the lake).

Inside the Sarano Tomb is a long corridor with doors to the left and right. The hunger isn't in the rooms on the left, but they do contain many tricky leveled enemies, which have good loot. The door on the right (where the hunger is) is locked and must be picked. The chest in the first room on the left is trapped.

Kill the hunger and the quest will be complete. Loot the body for the very valuable Sarano Ebony Helm. Once finished in the tomb return to Balmora.

Once returned speak to Eydis Fire-Eye, mention the Sarano Tomb, and she will give thanks for the Sarano family along with a reward of 1000 .

This is the end of the Balmora Fighters Guild quest-line and Eydis Fire-Eye will from now on say to speak to other guild leaders across Morrowind when asked for orders.

Eydis Fire-Eye told me a Hunger is loose in the Sarano Tomb which is over the hills southeast of the Fort Moonmoth between the Ashlands and Lake Amaya. I am ordered to travel to the tomb and kill the Hunger.